WASHINGTON (CNN) -- After wrapping up the longest presidential primary campaign in modern history, Sen. Hillary Clinton said Tuesday that she is ready to turn her attention back to being the junior senator from New York.

Sen. Hillary Clinton is greeted with cheers as she returns to the Senate after a two-week vacation.

"I look forward to being back with this great team," she said as she returned to the Senate at the end of a two-week vacation, taken after she conceded the 17-month-long primary contest to Sen. Barack Obama.

The second-term New York Democrat pledged to "immerse myself in there," pointing to the chamber.

She had just emerged from the party's weekly luncheon, which Senate Majority Leader Harry Reid called "one of the most emotional caucuses" he's ever attended on Capitol Hill.

He said the New York senator entered the event to a sea of high fives, cheers and a standing ovation from her Democratic colleagues.

"I come back with an even greater depth of awareness about what we have to do here in Washington," she said. "So many of the concerns that people have expressed to me over the course of this campaign are ones that they can't individually solve. They can't even really take it on just at the state or local level."

Clinton said that in addition to working "very hard to elect Sen. Obama our president," she plans to campaign on behalf of Democratic Senate candidates.

"We have been unfortunately stymied by the stalling tactics" of Republicans, she said, noting the need for 60 votes to get any legislation passed in the Senate.

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"It's going to be up to the Democratic Party, and particularly the Democratic Senate, to make progress on everything from health care and the economy to ending the war in Iraq," she said. "I look forward to being back with this great team that we have here and doing everything I can to make that happen."

Clinton said she is not spending time on the possibility that she may be asked to fill the No. 2 spot on Sen. Barack Obama's presidential ticket.

"You know, it is not something that I think about," she said. "This is totally Sen. Obama's decision, and that's the way it should be."

But she made clear, as she tried to do in her ultimate concession speech June 7, that her supporters should not stray toward John McCain, no matter any hard feelings left over from a bruising primary.

"Anyone who voted for me has very little in common with the Republican Party," she said.

Thursday night, Obama and Clinton are set to meet with key donors in Washington. The next day, the two will appear jointly in Unity, New Hampshire, a small town on that state's western border where the two candidates tied in the January primary.

"This is going to be a symbolic event that I hope will rally the Democratic Party behind the nominee," she said.

Obama said he looked forward to working with Clinton and her husband, former President Clinton, on his campaign for the White House.

"Bill Clinton is one of the most intelligent, charismatic political leaders that we have seen in a generation, and he has got a lot of wisdom to impart," Obama said Tuesday.

"We are going to be working very closely with him and Sen. Clinton to make sure that we not only win in November, but we actually govern in a way that delivers on the promise of universal health care, good jobs and good wages, clean energy, lower gas prices, the things that are really going to make an impact on people's lives," he said. Watch Obama discuss Clintons' role »

Obama said the senator's presidential campaign had "enhanced" her stature in a way that would bolster her efficacy in the Senate.

"She garnered not just votes but passion and support of so many millions of people," Obama said. "She's going to be a force to be reckoned with not only in the Senate, but hopefully, if I'm successful in the White House, she's going to be one of my key partners in making sure that were moving forward on issues like healthcare that she cares so deeply about."

At an event in Riverside, California, Sen. John McCain, the presumptive Republican presidential nominee, said Clinton is probably returning to the Senate with greater political clout.

"I think, if I had to guess, that the fact that the she ran an honorable and incredibly long and dedicated campaign for the nomination of her party would indicate to me that she would probably return to the United States senate with enhanced prestige and enhanced influence," McCain said.

He also praised Clinton for her work on military matters since joining the legislative body in 2001.

"I think that Sen. Clinton has already attained a position of leadership in the United States Senate," he said. "She works hard at her job. She is a very important member of the Armed Services Committee, and I have worked together with her on a variety of national security issues."

McCain is working hard to persuade Clinton supporters to back his campaign.